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In n gt 7 prove that ""^(n-1)C(3)+""^(n-...

In `n gt 7` prove that `""^(n-1)C_(3)+""^(n-1)C_(4) gt ""^(n)C_(3)`

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Prove that if ngt7 then .^(n-1)C_(3)+.^(n-1)C_(4)gt^(n)C_(3)

If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)(1+x)^(n-3) , prove that ""^(n)C_(r)=""^(n-2)C_(r)+3*""^(n-3)C_(r-1)*""^(n-3)C_(r-2)+""^(n-3)C_(r-3)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that C_(0) *""^(2n)C_(n) - C_(1) *""^(2n-2)C_(n) + C_(2) *""^(2n-4) C_(n) -…= 2^(n)

If .^(n)C_(4)=.^(n)C_(2) , then find .^(n)C_(3) .

If .^(n)C_(5)=.^(n)C_(4) , then find .^(n)C_(7) .

If ninNN , then by principle of mathematical induction prove that, .^(n)C_(0)+.^(n)C_(1)+.^(n)C_(2)+ . . .+.^(n)C_(n)=2^(n)(ninNN)

If .^(n)C_(5)=.^(n)C_(3) , then find .^(n)C_(4) .

Prove that "^n C_r+^(n-1)C_r+...+^r C_r=^(n+1)C_(r+1) .

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
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  2. A bag contains 50 tickets 1,2,3,...50 of which 5 are drawn at random a...

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  3. In n gt 7 prove that ""^(n-1)C(3)+""^(n-1)C(4) gt ""^(n)C(3)

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  4. If (""^(n)C(r-1))/(a)=(""^(n)C(r))/(b)=(""^(n)C(r))/(c) prove that n=(...

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  11. Show that the sum of the numbers in the n th bracket of the series (1)...

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  12. Show that the following two A.P. is have 14 common terms 3,7,11,15...,...

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  13. Show that there are 17 identical terms in the following two A.P. 2,5,8...

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